{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:CXDWIC7FZUYDQ35QQNGRQKM5EG","short_pith_number":"pith:CXDWIC7F","canonical_record":{"source":{"id":"math/0508020","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-07-31T18:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"7923f6ddeaa9178bae68908549490f95e988e44bf944770018b41afa9c631ee4","abstract_canon_sha256":"294b2222ae7de561a52523d32cf476399b49b2135d7c139ce3463bd127b1cd08"},"schema_version":"1.0"},"canonical_sha256":"15c7640be5cd30386fb0834d18299d21853a37feeb79e0ae0c0c62ea853556e0","source":{"kind":"arxiv","id":"math/0508020","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508020","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508020v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508020","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"CXDWIC7FZUYD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CXDWIC7FZUYDQ35Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CXDWIC7F","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:CXDWIC7FZUYDQ35QQNGRQKM5EG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0508020","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2005-07-31T18:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"7923f6ddeaa9178bae68908549490f95e988e44bf944770018b41afa9c631ee4","abstract_canon_sha256":"294b2222ae7de561a52523d32cf476399b49b2135d7c139ce3463bd127b1cd08"},"schema_version":"1.0"},"canonical_sha256":"15c7640be5cd30386fb0834d18299d21853a37feeb79e0ae0c0c62ea853556e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:40.118992Z","signature_b64":"Cd8r+lCmVKYkUGXmcM7Yx9VcIN9BvHy9fu+wspELpMvSURc3AD8hqi9aJo2bwdiGP9EF9V0GlA6pUYI0EUo8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15c7640be5cd30386fb0834d18299d21853a37feeb79e0ae0c0c62ea853556e0","last_reissued_at":"2026-05-18T00:42:40.118302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:40.118302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0508020","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3ZSibNKAgjZfMsmnO+cvhLtx/C52AUxFAKxmmz4j1TwaQLkEa3lTYg41ZNRYEPRdoBZO34Ht3/+rpl9ccWcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:36:13.525932Z"},"content_sha256":"73a5099dbcd049fedab0d4ead5de4cfb8b6e4c470699abf316bb7f5f94c5bdcd","schema_version":"1.0","event_id":"sha256:73a5099dbcd049fedab0d4ead5de4cfb8b6e4c470699abf316bb7f5f94c5bdcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:CXDWIC7FZUYDQ35QQNGRQKM5EG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An efficient shooting algorithm for Evans function calculations in large systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jeffrey Humpherys, Kevin Zumbrun","submitted_at":"2005-07-31T18:03:20Z","abstract_excerpt":"In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For small systems, a fast, shooting algorithm may be obtained by representing subspaces as single exterior products \\cite{AS,Br.1,Br.2,BrZ,BDG}. For large systems, however, the dimension of the exterior-product space quickly becomes prohibitive, growing as $\\binom{n}{k}$, where $n$ is the dimension of the system written as a first-order ODE and $k$ (typically $\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508020","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jpPQatYyHPGKMfQK9q1OX3rsdhRYc/GkUBL4PbIwphHw5fl2daFRUPpnvwy0BC+8/TiVDgo8VTPKz4jkflcVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:36:13.526263Z"},"content_sha256":"d027e0e2581cf2296a6eeec8d39b8c31635247dc07bd7dbc4d93338e84316932","schema_version":"1.0","event_id":"sha256:d027e0e2581cf2296a6eeec8d39b8c31635247dc07bd7dbc4d93338e84316932"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/bundle.json","state_url":"https://pith.science/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T13:36:13Z","links":{"resolver":"https://pith.science/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG","bundle":"https://pith.science/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/bundle.json","state":"https://pith.science/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXDWIC7FZUYDQ35QQNGRQKM5EG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:CXDWIC7FZUYDQ35QQNGRQKM5EG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"294b2222ae7de561a52523d32cf476399b49b2135d7c139ce3463bd127b1cd08","cross_cats_sorted":[],"license":"","primary_cat":"math.NA","submitted_at":"2005-07-31T18:03:20Z","title_canon_sha256":"7923f6ddeaa9178bae68908549490f95e988e44bf944770018b41afa9c631ee4"},"schema_version":"1.0","source":{"id":"math/0508020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508020","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508020v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508020","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"CXDWIC7FZUYD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CXDWIC7FZUYDQ35Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CXDWIC7F","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d027e0e2581cf2296a6eeec8d39b8c31635247dc07bd7dbc4d93338e84316932","target":"graph","created_at":"2026-05-18T00:42:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In Evans function computations of the spectra of asymptotically constant-coefficient linear operators, a basic issue is the efficient and numerically stable computation of subspaces evolving according to the associated eigenvalue ODE. For small systems, a fast, shooting algorithm may be obtained by representing subspaces as single exterior products \\cite{AS,Br.1,Br.2,BrZ,BDG}. For large systems, however, the dimension of the exterior-product space quickly becomes prohibitive, growing as $\\binom{n}{k}$, where $n$ is the dimension of the system written as a first-order ODE and $k$ (typically $\\s","authors_text":"Jeffrey Humpherys, Kevin Zumbrun","cross_cats":[],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-07-31T18:03:20Z","title":"An efficient shooting algorithm for Evans function calculations in large systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508020","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:73a5099dbcd049fedab0d4ead5de4cfb8b6e4c470699abf316bb7f5f94c5bdcd","target":"record","created_at":"2026-05-18T00:42:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"294b2222ae7de561a52523d32cf476399b49b2135d7c139ce3463bd127b1cd08","cross_cats_sorted":[],"license":"","primary_cat":"math.NA","submitted_at":"2005-07-31T18:03:20Z","title_canon_sha256":"7923f6ddeaa9178bae68908549490f95e988e44bf944770018b41afa9c631ee4"},"schema_version":"1.0","source":{"id":"math/0508020","kind":"arxiv","version":1}},"canonical_sha256":"15c7640be5cd30386fb0834d18299d21853a37feeb79e0ae0c0c62ea853556e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15c7640be5cd30386fb0834d18299d21853a37feeb79e0ae0c0c62ea853556e0","first_computed_at":"2026-05-18T00:42:40.118302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:40.118302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cd8r+lCmVKYkUGXmcM7Yx9VcIN9BvHy9fu+wspELpMvSURc3AD8hqi9aJo2bwdiGP9EF9V0GlA6pUYI0EUo8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:40.118992Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a5099dbcd049fedab0d4ead5de4cfb8b6e4c470699abf316bb7f5f94c5bdcd","sha256:d027e0e2581cf2296a6eeec8d39b8c31635247dc07bd7dbc4d93338e84316932"],"state_sha256":"2467d8a00955a704e7edea273534711ce57db76d0c1d24962511bae1b738e371"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5kCi4oYDRWSaTxCoZ6eFzRg2Kl3tfrHAQCj5Cu/AzIab/R/Unhbwzh163BO1UAN7jIlVrT6LexmzbRhipTBlCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:36:13.528119Z","bundle_sha256":"52d71902fd1a80e9cea24bc2010dd946e604efbdcac761b5367ab7b3a7729ab0"}}